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Area of Science:

  • Quantum Information Science
  • Quantum Computation
  • Continuous-Variable Quantum Computing

Background:

  • Physical Gottesman-Kitaev-Preskill (GKP) states are essential for quantum error correction but are inherently noisy.
  • Ideal GKP states require infinite energy, making practical implementation challenging.
  • Noise in GKP states is typically viewed as a limitation to be corrected.

Purpose of the Study:

  • To demonstrate that imperfect GKP stabilizer states can be leveraged for quantum computation.
  • To show how non-Clifford gates can be implemented using linear optical elements and imperfect GKP states.
  • To establish a practical framework for achieving computational universality in continuous-variable quantum computation.

Main Methods:

  • Utilizing Gaussian operations on normalizable GKP states.
  • Employing homodyne measurements.
  • Implementing clean projection onto Pauli eigenstates within the GKP code space.
  • Achieving probabilistic projection of unmeasured modes onto non-Pauli eigenstates.

Main Results:

  • Demonstrated high-fidelity implementation of Clifford gates using imperfect GKP states.
  • Showcased probabilistic implementation of non-Pauli eigenstates, crucial for universal computation.
  • Established that imperfect GKP states, combined with Gaussian operations and homodyne measurements, enable key computational primitives.
  • Provided a practical pathway towards computational universality in continuous-variable quantum computation.

Conclusions:

  • Imperfect GKP stabilizer states are not merely a deficiency but a resource for quantum computation.
  • Gaussian operations and homodyne measurements on normalizable GKP states facilitate universal quantum computation.
  • This work presents a realistic framework for measurement-based quantum computation in continuous-variable systems.